MathDB

The

27

points

(a,b,c)

of the space are marked such that

a

b

and

c

take the values

0

1

2

. We will call these points "junctures". Using

54

rods of length

1

, all the joints that are at a distance of

1

are joined together. A cubic structure of

2\times 2\times 2

is thus formed. An ant starts from a juncture

A

and moves along the rods; When it reaches a juncture it turns

90^\circ

and changes rod. If the ant returns to

A

and has not visited any juncture more than once except

A

, which it visited

2

times, at the beginning of the walk and at the end of it, what is the greatest length that the path of the ant can have?

Problem Statement